Related papers: Asymptotics in Knuth's parking problem for caravan…
Black holes appear as vacuum solutions of classical general relativity which depend on Newton's constant and possibly the cosmological constant. At the level of a quantum field theory, these coupling constants typically acquire a…
This work focuses on quantitative representation of transport in systems with quenched disorder. Explicit mapping of the quenched trap model to continuous time random walk is presented. Linear temporal transformation: $t\to…
We consider multi-component matching systems in heavy traffic consisting of $K\geq 2$ distinct perishable components which arrive randomly over time at high speed at the assemble-to-order station, and they wait in their respective queues…
Given a positive-integer-valued vector $u=(u_1, \dots, u_m)$ with $u_1<\cdots<u_m$. A $u$-parking function of length $m$ is a sequence $\pi=(\pi_1, \dots, \pi_m)$ of positive integers whose non-decreasing rearrangement $(\lambda_1, \dots,…
Recently, the authors extended the notion of parking functions to parking sequences, which include cars of different sizes, and proved a product formula for the number of such sequences. We here give a refinement of that result involving…
We investigate pathwise turnpike behavior of discrete-time stochastic linear-quadratic optimal control problems. Our analysis is based on a novel strict dissipativity notion for such problems, in which a stationary stochastic process…
The random flights are (continuous time) random walkswith finite velocity. Often, these models describe the stochastic motions arising in biology. In this paper we study the large time asymptotic behavior of random flights. We prove the…
This article is concerned with the asymptotic behavior of a 2D overhead crane. Taking into account the presence of a delay in the boundary, and assuming that no displacement term appears in the system, a distributed (interior) damping…
Recent advances in multiagent simulations have made possible the study of realistic traffic patterns and allow to test theories based on driver behaviour. Such simulations also display various empirical features of traffic flows, and are…
In the framework of the semiclassical approach the universal spectral correlations in the Hamiltonian systems with classical chaotic dynamics can be attributed to the systematic correlations between actions of periodic orbits which (up to…
Disorder in a 1D quantum lattice induces Anderson localization of the eigenstates and drastically alters transport properties of the lattice. In the original Anderson model, the addition of a periodic driving increases, in a certain range…
Smart-parking solutions use sensors, cameras, and data analysis to improve parking efficiency and reduce traffic congestion. Computer vision-based methods have been used extensively in recent years to tackle the problem of parking lot…
We explore the link between combinatorics and probability generated by the question "What does a random parking function look like?" This gives rise to novel probabilistic interpretations of some elegant, known generating functions. It…
In this paper we study the asymptotic behavior of a random uniform parking function $\pi_n$ of size $n$. We show that the first $k_n$ places $\pi_n(1),\dots,\pi_n(k_n)$ of $\pi_n$ are asymptotically i.i.d. and uniform on $\{1,2,\dots,n\}$,…
We study the number of collisions $X_n$ of an exchangeable coalescent with multiple collisions ($\Lambda$-coalescent) which starts with $n$ particles and is driven by rates determined by a finite characteristic measure $\nu({\rm…
The parking-lot model provides a qualitative description of the main features of the phenomenology of granular compaction. We derive here approximate kinetic equations for this model, equations that are based on a $2-$parameter…
We study the kinetics of competitive random sequential adsorption (RSA) of particles of binary mixture of points and fixed-sized particles within the mean-field approach. The present work is a generalization of the random car parking…
We investigate the asymptotic behavior of the nonautonomous evolution problem generated by the Klein-Gordon equation in an expanding background, in one space dimension with periodic boundary conditions, with a nonlinear potential of…
In this paper, we obtain asymptotic formulas for an infinite class of rank generating functions. As an application, we solve a conjecture of Andrews and Lewis on inequalities between certain ranks.
Let $(A_u : u \in \mathbb{B})$ be i.i.d.~non-negative integers that we interpret as car arrivals on the vertices of the full binary tree $ \mathbb{B}$. Each car tries to park on its arrival node, but if it is already occupied, it drives…